Dual F-signature

TL;DR

This paper introduces the dual F-signature, an invariant for modules that generalizes the F-signature of rings, and uses it to characterize various singularities in algebraic geometry.

Contribution

It defines the dual F-signature for modules and applies it to characterize regular, F-regular, F-rational, and Gorenstein singularities.

Findings

Dual F-signature coincides with F-signature for the base ring.

Characterizations of singularities using the dual F-signature.

Provides new tools for understanding singularities in algebraic geometry.

Abstract

We define the dual F-signature of modules, which is equivalent to the F-signature if the module is the base ring. By using this invariant, We give characterizations of regular, F-regular, F-rational, and Gorenstein singularities.